Journal Article10.1007/S11075-020-00888-8
Convergence analysis on matrix splitting iteration algorithm for semidefinite linear complementarity problems
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TL;DR: The modulus-based matrix splitting iteration methods, which are obtained by reformulating equivalently SDLCP as an implicit fixed-point matrix equation, are established.
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Abstract: In this paper, we present some novel observations for the semidefinite linear complementarity problems, abbreviated as SDLCPs. Based on these new results, we establish the modulus-based matrix splitting iteration methods, which are obtained by reformulating equivalently SDLCP as an implicit fixed-point matrix equation. The convergence of the proposed modulus-based matrix splitting iteration methods has been analyzed. Numerical experiments have shown that the modulus-based iteration methods are effective for solving SDLCPs.
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Citations
A two-step new modulus-based matrix splitting method for vertical linear complementarity problem
Cuixia Li,Shiliang Wu +1 more
TL;DR: A two-step modulus-based matrix splitting method is introduced for solving the vertical linear complementarity problem, with convergence properties discussed and numerical experiments confirming its superiority over existing methods.
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A preconditioned new modulus-based matrix splitting method for solving linear complementarity problem of $ H_+ $-matrices
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TL;DR: A comparison theorem is provided to theoretically show the PNMMS method accelerates the convergence rate and a generalized preconditioner is devised that is associated with both H_+ and A of the linear complementarity problem.
Modulus-based matrix splitting iteration methods with new splitting scheme for horizontal implicit complementarity problems
TL;DR: In this article , the authors reformulated the horizontal implicit complementarity problem as an implicit fixed-point equation, and applied the modulus-based matrix splitting iteration methods to solve the problems.
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